As I recall, select fire was originally planned for the M1 Carbine in the design phase - I'm not clear on why it was not provided initially.
Lots of inventions, worldwide seem to pop up in different places at about the same time - because the world wide technology to produce it becomes available, and the old thinking of how to do something is being challanged in several places at once.
But sometimes you can trace the "Father" pretty accurately. US Army Air Corps officer Claire Chennault, later of Flying Tigers fame, developed a staged "distant early warning net" in Hawaii before he even had radar - then used it again in China, and pioneered the Paratroop concept, doing actual drop trials with US soldiers and their equipment using biplanes and Ford Trimotors.
A visiting Russian Military Delegation watched one of Chennault's early experiments at dropping US Army troops and equipment - and Russia immediately offered Chennault a job! When he refused, they immediately developed their own Paratroops, then shared the concept with their new found friends, the Germans. Many think it was a Russian or German concept - because we were slower to promote it! "A Prophet is without honor in his own country". CC
Colt, Glock and Remington factory trained LE Armorer
LE Trained Firearms Instructor